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Find Equivalent Ratio for 52/80 with Whole 100 to Calculate Corn Sales Percentage
Mathematics
Grade 6 (Primary School)
Question Content
Isabelle sells corn at her family's produce stand. On Saturday, Isabelle sells 52 out of 80 ears of corn. She wants to know what percent of the total amount of corn she sold. Now, find an equivalent ratio where the total number of ears of corn is 100. Fill in the missing value in the table: Number of Ears of Corn Sold (Part): 13, 52, [?]; Total Number of Ears of Corn (Whole): 20, 80, 100
Correct Answer
65
Detailed Solution Steps
1
Step 1: Identify the given ratio we need to convert: the ratio of sold corn to total corn is 52:80.
2
Step 2: Set up a proportion to find the equivalent part when the whole is 100. Let x be the number of sold corn in the equivalent ratio. The proportion is $\\frac{52}{80} = \\frac{x}{100}$.
3
Step 3: Solve for x using cross-multiplication: $80x = 52 \\times 100$. Calculate $52 \\times 100 = 5200$, so $80x = 5200$.
4
Step 4: Divide both sides by 80 to isolate x: $x = \\frac{5200}{80} = 65$.
5
Alternative Step: Simplify the original ratio first. $\\frac{52}{80}$ simplifies to $\\frac{13}{20}$ by dividing numerator and denominator by 4. Then multiply numerator and denominator by 5 to get a denominator of 100: $\\frac{13 \\times 5}{20 \\times 5} = \\frac{65}{100}$, so the missing value is 65.
Knowledge Points Involved
1
Equivalent Ratios
Equivalent ratios are ratios that have the same proportional relationship between two quantities. They can be found by multiplying or dividing both the numerator and denominator of a ratio by the same non-zero number. This is used to scale ratios up or down while keeping the relationship consistent.
2
Proportions
A proportion is an equation that states two ratios are equal, written as $\\frac{a}{b} = \\frac{c}{d}$. Cross-multiplication (where $ad = bc$) is a method used to solve for unknown values in a proportion, which is essential for finding equivalent ratios with a specified denominator or numerator.
3
Percent as a Ratio to 100
A percent is a ratio that compares a number to 100. Converting a part-to-whole ratio to a ratio with a denominator of 100 directly gives the percentage value, where the numerator is the percent number. For example, $\\frac{65}{100}$ is equal to 65%.
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